(5x-4)(2x-7)=0

Solution for (5x-4)(2x-7)=0 equation:

(5x-4)(2x-7)=0

We multiply parentheses ..

(+10x^2-35x-8x+28)=0

We get rid of parentheses

10x^2-35x-8x+28=0

We add all the numbers together, and all the variables

10x^2-43x+28=0

a = 10; b = -43; c = +28;
Δ = b2-4ac
Δ = -432-4·10·28
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-27}{2*10}=\frac{16}{20}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+27}{2*10}=\frac{70}{20}
=3+1/2
$